Artificial Electric Field Algorithm

AEFA.m

function [Fbest,Lbest,BestValues,MeanValues]=AEFA(func_num,N,max_it,FCheck,tag,Rpower)
%V:   Velocity.
%a:   Acceleration.
%Q:   Charge  
%D:   Dimension of the test function.
%N:   Number of charged particles.
%X:   Position of particles.
%R:   Distance between charged particle in search space.
%lb:  lower bound of the variables
%ub:  upper bound of the variables
%Rnorm: Euclidean Norm 
Rnorm=2; 
% Dimension and lower and upper bounds of the variables
[lb,ub,D]=benchmark_range(func_num);  
%------------------------------------------------------------------------------------
%random initialization of charge population.
%X=initialization(D,N,ub,lb); 
X=rand(N,D).*(ub-lb)+lb;
%create the best so far chart and average fitnesses chart.
BestValues=[];MeanValues=[];
V=zeros(N,D);
%-------------------------------------------------------------------------------------
for iteration=1:max_it
    
%Evaluation of fitness values of charged particles. 
 for i=1:N 
    %calculation of objective function for charged particle 'i'
    fitness(i)=benchmark(X(i,:),func_num,D);
 end
 
 %fitness =benchmark(X,func_num,D);
 
    if tag==1
    [best, best_X]=min(fitness); %minimization.
    else
    [best, best_X]=max(fitness); %maximization.
    end        
    if iteration==1
       Fbest=best;Lbest=X(best_X,:);
    end
    if tag==1
      if best<Fbest  %minimization.
       Fbest=best;Lbest=X(best_X,:);
      end
    else 
      if best>Fbest  %maximization
       Fbest=best;Lbest=X(best_X,:);
      end
    end
    
BestValues=[BestValues Fbest];
MeanValues=[MeanValues mean(fitness)];
%-----------------------------------------------------------------------------------
% Charge 
Fmax=max(fitness); Fmin=min(fitness); Fmean=mean(fitness); 
if Fmax==Fmin
   M=ones(N,1);
   Q=ones(N,1);
else
    
   if tag==1 %for minimization
      best=Fmin;worst=Fmax; 
      
   else %for maximization
       
      best=Fmax;worst=Fmin; 
   end
  
   Q=exp((fitness-worst)./(best-worst)); 
end
Q=Q./sum(Q); 
%----------------------------------------------------------------------------------
fper=3; %In the last iteration, only 2-6 percent of charges apply force to the others.
%----------------------------------------------------------------------------------
 %%%%total electric force calculation
 if FCheck==1
     cbest=fper+(1-iteration/max_it)*(100-fper); 
     cbest=round(N*cbest/100);
 else
     cbest=N; 
 end
    [Qs s]=sort(Q,'descend');
 for i=1:N
     E(i,:)=zeros(1,D);
     for ii=1:cbest
         j=s(ii);
         if j~=i
            R=norm(X(i,:)-X(j,:),Rnorm); %Euclidian distanse.
         for k=1:D 
             E(i,k)=E(i,k)+ rand*(Q(j))*((X(j,k)-X(i,k))/(R^Rpower+eps));
              
         end
         end
     end
 end
%---------------------------------------------------------------------------------- 
%Calculation of Coulomb constant
%----------------------------------------------------------------------------------
alfa=30;K0=500;
K=K0*exp(-alfa*iteration/max_it);
%---------------------------------------------------------------------------------- 
%%%Calculation of accelaration.
a=E*K; 
%----------------------------------------------------------------------------------
%Charge movement
%----------------------------------------------------------------------------------
V=rand(N,D).*V+a;
X=X+V;
X=max(X,lb);X=min(X,ub);   % Check the bounds of the variables
%----------------------------------------------------------------------------------
%plot charged particles 
%mask it if you do not need to plot them
%----------------------------------------------------------------------------------
swarm(1:N,1,1)=X(:,1);
swarm(1:N,1,2)=X(:,2);
clf    
    plot(swarm(:, 1, 1), swarm(:, 1, 2), 'X')  % drawing swarm movements
    hold on;
    plot(swarm(best_X,1,1),swarm(best_X,1,2),'*r') % drawning of best charged particle
    axis([lb ub lb ub]);
     title(['\fontsize{12}\bf Iteration:',num2str(iteration)]);
pause(.2)
%---------------------------------------------------------------------------------
end 
end

benchmark.m

function fit=benchmark(X,func_num,D)
% New functions may be added in this file
if func_num==1
fit=sum(X.^2);
end
if func_num==2 
fit=sum(abs(X))+prod(abs(X));
end
return

benchmark_range

% This function gives boundaries and dimension of search space for test functions.
function [lb,ub,D]=benchmark_range(func_num)
%If lower bounds of dimensions are the same, then 'lb' is a value.
%Otherwise, 'lb' is a vector that shows the lower bound of each dimension.
%This is also true for upper bounds of dimensions.
%Insert your own boundaries with a new func_num.
if func_num==1
    lb=-100;ub=100;D=30;
end
if func_num==2
    lb=-10;ub=10;D=30;
end

Main.m

% "AEFA: Artificial electric field algorithm for global optimization." Swarm and Evolutionary Computation 48, pp. 93-108 (2019). 
% Anupam Yadav 14.04.2018, Department of Mathematics, NIT Jalandhar
% anupuam@gmail.com
clear all;
clc;
for i=1:1
rng('default');
rng(1);
 N=50; 
 max_it=1000; 
 FCheck=1; R=1;
 tag=1; % 1: minimization, 0: maximization
 rand('seed', sum(100*clock));
 func_num=i
 [Fbest,Lbest,BestValues,MeanValues]=AEFA(func_num,N,max_it,FCheck,tag,R);Fbest,
%  semilogy(BestValues,'--r');
%  title(['\fontsize{12}\bf F',num2str(func_num)]);
%  xlabel('\fontsize{12}\bf Iteration');ylabel('\fontsize{12}\bf Best-so-far');
%  legend('\fontsize{10}\bf AEFA',1);
end